Experimental High-Accuracy and Broadband Quantum Frequency Sensing via Geodesic Control

Accurate frequency estimation of oscillating signals over a broad bandwidth is a central task in quantum sensing, yet it is often compromised by spurious responses to higher-order harmonics in realistic multi-frequency environments. Here we experimentally demonstrate a high-accuracy and broadband quantum frequency sensing protocol based on geodesic control, implemented using the electron spin of a single nitrogen-vacancy center in diamond. By engineering an intrinsically single-frequency response, geodesic control enables bias-free frequency estimation with strong suppression of harmonic-induced systematic errors across a wide spectral range spanning from the megahertz to the gigahertz regime. Furthermore, by incorporating synchronized readout, we achieve millihertz-level frequency resolution under noisy signal conditions. Our results provide systematic experimental benchmarking of geodesic control for quantum frequency sensing and establish it as a practical approach for high-accuracy metrology in realistic environments.

💡 Research Summary

The authors present an experimental demonstration of a high‑accuracy, broadband quantum frequency‑sensing protocol based on “geodesic control,” implemented with the electron spin of a single nitrogen‑vacancy (NV) center in diamond. Conventional dynamical‑decoupling (DD) sequences such as CPMG or XY families provide narrow‑band sensitivity to a target AC frequency ωₛ but inevitably retain appreciable response to odd‑order harmonics (k = 3, 5, 7,…). These spurious harmonics generate systematic biases that limit frequency‑metrology performance in realistic multi‑frequency environments.

Geodesic control addresses this limitation by engineering the control trajectory itself. The protocol consists of a train of π‑pulses whose rotation axes rotate continuously in time according to ϕⱼ = 2πTⱼ/T_scan. In the interaction picture the resulting modulation function approaches a pure cosine, F_GD(t) ≈ cos(2πt/T_scan), so the sensor’s effective Hamiltonian couples only to the component of the external magnetic field that oscillates at the scanning frequency ω_scan = 2π/T_scan. When ω_scan matches the target frequency ωₛ (or the detuning Δₛ in the heterodyne configuration), the accumulated phase Φ_GD builds up constructively; for all other frequencies, including higher‑order harmonics, the phase averages to zero.

Two experimental regimes are explored. In the megahertz (MHz) band the parallel magnetic component B∥(t) is sensed using the GD∥ sequence; in the gigahertz (GHz) band the perpendicular component B⊥(t) is heterodyned to a low‑frequency detuning Δₛ and sensed with the GD⊥ sequence. The authors reconstruct the Fourier spectra of the modulation functions and show that GD∥/GD⊥ exhibit a dominant peak at the intended scan frequency with harmonic side‑lobes suppressed by more than three orders of magnitude, whereas XY and CPMG retain sizable harmonic peaks.

Robustness against multi‑frequency noise is quantified by adding controlled noise tones at ω_n = k ω_scan (k = 3, 5, 7) with amplitudes up to 2π × 85 kHz. Under these conditions the final‑state fidelity remains above 0.9 for the geodesic protocols, while it rapidly degrades for XY/CPMG. Frequency‑estimation experiments with simultaneous noise tones reveal that the conventional DD schemes produce multiple resonance dips and biases of 8–9 kHz, whereas the geodesic protocols yield a single, unbiased dip with sub‑2 kHz bias. The full‑width at half‑maximum of the resonance is 15 kHz (GD∥) and 33 kHz (GD⊥), narrower than the corresponding DD results.

To push spectral resolution, the authors integrate synchronized readout, repeatedly measuring the NV fluorescence with sub‑100 µs repetition periods over tens of minutes. Fourier analysis of the time‑trace achieves a frequency resolution of 1 mHz for GD∥ and 2 mHz for GD⊥, far surpassing the ~kHz resolution of conventional DD under the same conditions.

Overall, the work demonstrates that geodesic control provides (i) intrinsic single‑frequency selectivity that eliminates harmonic‑induced systematic errors, (ii) broadband operation from MHz to GHz by exploiting both parallel and perpendicular magnetic components, and (iii) compatibility with high‑resolution techniques such as synchronized readout. These attributes make geodesic control a practical, scalable tool for quantum metrology tasks that demand high accuracy and robustness in realistic, noisy environments, including nanoscale NMR, microwave photon entanglement detection, and advanced radar or communication diagnostics.